Tagged Questions

Mathematical intuition is the instinctive impression regarding mathematical ideas which originate naturally without regard to formal mathematical proofs. It may or may not stem from a cognitive rational process.

I Have a problem. I mostly do mathematics because I find it fascinating and enjoy doing it. Now whenever I skim through a book a number theory I always find myself thinking 'I wish I would understand ...

The self-information of an outcome $x_i$, or surprisal, is defined as:
$$
I(x_i)=-\log P(x_i),
$$
where $P$ means probability. This way, the Shannon entropy can be seen as the "average" or "expected" ...

I know the formal definitions of both continuous map and a homeomorphism between two spaces.
If two spaces are homeomorphic intuitively they can be thought of spaces which can converted to each other ...

I'm a 17 years old and I have no clue about a concept known as limit cycles. I looked it up and I understand it represents the orbit of functions approaching other A person told me that limit cycles ...

I have a problem about intuition:
substracting the mean of iid RVs seems to increase the mutual information.
Say $X,Y$ are real iid RVs, then $\frac{X-Y}{2}$ and $\frac{Y-X}{2}$ are not independent ...

Easter Sunday is the first Sunday after the first full moon of spring. Given just the year, Gauss was able to derive a formula which gave you the month and day that easter sunday fell on. The formula ...

So I understand that when dy/dt is 0, this means that $y(t)$ is a constant. But why does the number of limiting behavior depend on the roots of the differential equation. And why if $dy/dt ≠ 0$, the ...

I have to give a presentation on the theorem in Real Analysis with a fellow student. While I've looked over the proof and verified that, yes, step B does indeed follow logically from step A, etc. and ...

Although this question might sound a little too simple, it is a problem that I must get addressed. In addition, there is no way for me to formally describe it. If you have something you can add, by ...

An approach to chain homotopies, alternative to the usual boundary relation, uses the monoidal (closed) structure of $\mathsf{Ch}_\bullet(R\mathsf{Mod})$ with $R$ a commutative ring. In particular, a ...

We know examples of functions (obviously we are in the context of real valued functions) which are continous but not derivable; the simplest is $x\mapsto|x|$. In particular we have a precise graphic ...

Is there some intuition as to why ill conditioned system of equations hard to solve iteratively ( i.e. the convergence is slow) ? I've read convergence proofs of several methods, but still don't have ...

I'm new and this is my first question (though I've been lurking). English is not my native language. Studying on my own.
I'm really interested in deriving the formula $1^{2} + 2^{2} + 3^{2} + \cdots+ ...

In number theory we have so-called explicit formula's in terms of the Riemann zeta zero's.
For instance to count the sum of the logarithms of the primes below some given integer.
( second Chebyshev ...

Usually, when using a Taylor series to describe a function (which may itself be a model of some physical phenomenon), we often throw out the higher order terms, as they are quite small relative to the ...